Compact operators on sequence spaces associated with the Copson matrix of order α
Abstract In this work, we study characterizations of some matrix classes ( C ( α ) ( ℓ p ) , ℓ ∞ ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ , ( C ( α ) ( ℓ p ) , c ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ , and ( C ( α ) ( ℓ p ) , c 0 ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ ,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02713-9 |
| _version_ | 1818688938840162304 |
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| author | M. Mursaleen Osama H. H. Edely |
| author_facet | M. Mursaleen Osama H. H. Edely |
| author_sort | M. Mursaleen |
| collection | DOAJ |
| description | Abstract In this work, we study characterizations of some matrix classes ( C ( α ) ( ℓ p ) , ℓ ∞ ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ , ( C ( α ) ( ℓ p ) , c ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ , and ( C ( α ) ( ℓ p ) , c 0 ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ , where C ( α ) ( ℓ p ) $\mathcal{C}^{(\alpha )}(\ell ^{p})$ is the domain of Copson matrix of order α in the space ℓ p $\ell ^{p}$ ( 0 < p < 1 $0< p<1$ ). Further, we apply the Hausdorff measures of noncompactness to characterize compact operators associated with these matrices. |
| first_indexed | 2024-12-17T12:02:10Z |
| format | Article |
| id | doaj.art-d3338ba0ab234756bde8694b2b94ae5c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-17T12:02:10Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d3338ba0ab234756bde8694b2b94ae5c2022-12-21T21:49:49ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-10-012021111010.1186/s13660-021-02713-9Compact operators on sequence spaces associated with the Copson matrix of order αM. Mursaleen0Osama H. H. Edely1Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan)Department of Mathematics, Tafila Technical UniversityAbstract In this work, we study characterizations of some matrix classes ( C ( α ) ( ℓ p ) , ℓ ∞ ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ , ( C ( α ) ( ℓ p ) , c ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ , and ( C ( α ) ( ℓ p ) , c 0 ) $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ , where C ( α ) ( ℓ p ) $\mathcal{C}^{(\alpha )}(\ell ^{p})$ is the domain of Copson matrix of order α in the space ℓ p $\ell ^{p}$ ( 0 < p < 1 $0< p<1$ ). Further, we apply the Hausdorff measures of noncompactness to characterize compact operators associated with these matrices.https://doi.org/10.1186/s13660-021-02713-9Sequence spacesCesàro matrixCopson matrixCopson matrix of order αMatrix transformationsHausdorff measure of noncompactness |
| spellingShingle | M. Mursaleen Osama H. H. Edely Compact operators on sequence spaces associated with the Copson matrix of order α Journal of Inequalities and Applications Sequence spaces Cesàro matrix Copson matrix Copson matrix of order α Matrix transformations Hausdorff measure of noncompactness |
| title | Compact operators on sequence spaces associated with the Copson matrix of order α |
| title_full | Compact operators on sequence spaces associated with the Copson matrix of order α |
| title_fullStr | Compact operators on sequence spaces associated with the Copson matrix of order α |
| title_full_unstemmed | Compact operators on sequence spaces associated with the Copson matrix of order α |
| title_short | Compact operators on sequence spaces associated with the Copson matrix of order α |
| title_sort | compact operators on sequence spaces associated with the copson matrix of order α |
| topic | Sequence spaces Cesàro matrix Copson matrix Copson matrix of order α Matrix transformations Hausdorff measure of noncompactness |
| url | https://doi.org/10.1186/s13660-021-02713-9 |
| work_keys_str_mv | AT mmursaleen compactoperatorsonsequencespacesassociatedwiththecopsonmatrixofordera AT osamahhedely compactoperatorsonsequencespacesassociatedwiththecopsonmatrixofordera |